Problem: All triangles have the same value, and all circles have the same value. What is the sum of three circles? \begin{align*}
\Delta + \bigcirc + \Delta + \bigcirc + \Delta&= 21\\
\bigcirc + \Delta+\bigcirc+\Delta+\bigcirc &= 19\\
\bigcirc + \bigcirc + \bigcirc &= \ ?
\end{align*}
Explanation: Replace a triangle with the letter $a$ and a circle with the letter $b.$ The two given equations become \begin{align*}
3a+2b&=21\\
2a+3b&=19.
\end{align*}Multiplying the first equation by $2,$ we get $6a+4b=42.$ Multiplying the second equation by $3,$ we get $6a+9b=57.$ Subtracting these two equations to eliminate $a,$ we have $5b=15.$ Multiplying both sides by $\frac{3}{5},$ we get $$\frac{3}{5}\cdot 5b = \frac{3}{5} \cdot 15 \Rightarrow 3b=9.$$Thus, three circles equals $\boxed{9}.$